Question : The height and the radius of the base of a right circular cone are in the ratio of 12 : 5. If its volume is 314 cm³, then what is the slant height of the cone? (Use $\pi$ = 3.14)
Option 1: 12 cm
Option 2: 11 cm
Option 3: 13 cm
Option 4: 14 cm

Question

Question : The height and the radius of the base of a right circular cone are in the ratio of 12 : 5. If its volume is 314 cm³, then what is the slant height of the cone? (Use $\pi$ = 3.14)

Option 1: 12 cm

Option 2: 11 cm

Option 3: 13 cm

Option 4: 14 cm

Team Careers360 · Accepted Answer

Correct Answer: 13 cm

Solution : Given: The height and the radius of the base of a right circular cone = 12 : 5
Let the height be $12x$ and the radius is $5x$.
Volume = 314 cm³
We know that,
Volume of a cone = $\frac{1}{3}\pi r^2 h$
⇒ $314 = \frac{1}{3} × 3.14 × 5x × 5x × 12x$
⇒ $100 = 100x^3$
⇒ $x=1$
Radius $=5x=5 imes1=5$
Height $=12x=12 imes1=12$
Slant height = $\sqrt{ ext{height$^2$ + radius$^2$}}=\sqrt{12^2+5^2}=\sqrt{144+25}=\sqrt{169}=13\ ext{cm}$
Hence, the correct answer is 13 cm.

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Question : The height and the radius of the base of a right circular cone are in the ratio of 12 : 5. If its volume is 314 cm3, then what is the slant height of the cone? (Use π = 3.14)Option 1: 12 cmOption 2: 11 cmOption 3: 13 cmOption 4: 14 cm

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Question : The height and the radius of the base of a right circular cone are in the ratio of 12 : 5. If its volume is 314 cm³, then what is the slant height of the cone? (Use $π$ = 3.14)
Option 1: 12 cm
Option 2: 11 cm
Option 3: 13 cm
Option 4: 14 cm